Basic Math Examples

$\frac{7}{9} + 1 \frac{1}{4}$

Step 1

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{7}{9} + 1 + \frac{1}{4}$

Step 1.2

Add $1$ and $\frac{1}{4}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{7}{9} + \frac{4}{4} + \frac{1}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{7}{9} + \frac{4 + 1}{4}$

Step 1.2.3

Add $4$ and $1$ .

$\frac{7}{9} + \frac{5}{4}$

Step 2

To write $\frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7}{9} \cdot \frac{4}{4} + \frac{5}{4}$

Step 3

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{7}{9} \cdot \frac{4}{4} + \frac{5}{4} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{9}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 4}{9 \cdot 4} + \frac{5}{4} \cdot \frac{9}{9}$

Step 4.2

Multiply $9$ by $4$ .

$\frac{7 \cdot 4}{36} + \frac{5}{4} \cdot \frac{9}{9}$

Step 4.3

Multiply $\frac{5}{4}$ by $\frac{9}{9}$ .

$\frac{7 \cdot 4}{36} + \frac{5 \cdot 9}{4 \cdot 9}$

Step 4.4

Multiply $4$ by $9$ .

$\frac{7 \cdot 4}{36} + \frac{5 \cdot 9}{36}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 4 + 5 \cdot 9}{36}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $4$ .

$\frac{28 + 5 \cdot 9}{36}$

Step 6.2

Multiply $5$ by $9$ .

$\frac{28 + 45}{36}$

Step 6.3

Add $28$ and $45$ .

$\frac{73}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{73}{36}$

Decimal Form:

$2.02\overline{7}$

Mixed Number Form:

$2 \frac{1}{36}$